Problem: $\lim_{x\to\pi}\cot(x)=?$ Choose 1 answer: Choose 1 answer: (Choice A) A $-1$ (Choice B) B $0$ (Choice C) C $1$ (Choice D) D The limit doesn't exist.
Solution: $\cot(x)$ is continuous on all points in its domain. Therefore, if $x=\pi$ is within the domain of $\cot(x)$, we can find $\lim_{x\to\pi}\cot(x)$ by direct substitution. $x=\pi$ is not in the domain of $\cot(x)$ : $\begin{aligned} \cot(\pi)&=\dfrac{\cos(\pi)}{\sin(\pi)} \\\\ &=\dfrac{-1}{0} \end{aligned}$ Since direct substitution ends with $\dfrac{-1}{0}$, we know that $\lim_{x\to\pi}\cot(x)$ doesn't exist.